Tracking Multiple Dynamic Targets with Multidimensional Scaling

Abstract

We consider the problem of tracking multiple targets in the presence of imperfect and incomplete ranging information, focusing on the impact of target dynamics. The targets are assumed to describe independent, continuous and differentiable trajectories with non-stationary (dynamic) statistics, i.e., with variable velocities and accelerations. The impact of such dynamics onto the performance, computational complexity and memory requirements of two tracking techniques, namely, the Kalman filter (KF) and multidimensional scaling (MDS), is investigated. The main feature of the MDS-based tracking algorithm, which we proposed in an earlier work, is that tracking is performed over the eigenspace of a Nystrom-Gram kernel matrix constructed with no a-priori knowledge of the statistics of target trajectories. Consequently, tracking becomes a problem of updating the eigenspace given new input data, which is achieved with an iterative Jacobian eigen-decomposition technique. An advantage of this technique over the KF is that tracking accuracy is independent on target dynamics. Furthermore, the number of iterations required to update the eigenspace, is shown to grow only logarithmically with the target dynamics and with the number of simultaneously tracked targets. As a result, the MDS-based tracking algorithm with Jacobian eigenspace updating becomes more efficient than the KF as soon as a relatively small number of targets are simultaneously tracked, and/or target dynamics exceeds a certain threshold.